The sum of the three angles in a triangle is 180° The sum of the four angles in a quadrilateral is 360°

∠A+∠B+∠C=180°

∠D+∠E+∠F+∠G=360°

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Slide 1: Slide

WiskundeMiddelbare schoolvwoLeerjaar 1

This lesson contains 10 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

Items in this lesson

Sum of the angles

The sum of the three angles in a triangle is 180° The sum of the four angles in a quadrilateral is 360°

∠A+∠B+∠C=180°

∠D+∠E+∠F+∠G=360°

Slide 1 - Slide

Calculating angles

You can use the sum of the angles and your knowledge of special triangles and quadrilaterals to calculate unknown angles.

Slide 2 - Slide

Calculating angles

Calculate the size of angle C.

Slide 3 - Slide

What size is angle C?

A

∠C=360−82−60=218°

B

∠C=82+60=142°

C

∠C=180−82−60=38°

D

∠C=3(82+60)=37°

Slide 4 - Quiz

Calculating angles

The angle sum of a triangle is 180°

∠C=180−82−60=38°

Slide 5 - Slide

Calculating angles

Quadrilateral DEFG is a rhombus. Calculate the size of angle G.

Slide 6 - Slide

What size is angle G?

A

∠G=245°

B

∠G=115°

C

∠G=65°

D

∠G=57.5°

Slide 7 - Quiz

Calculating angles

Quadrilateral DEFG is a rhombus The angle sum of a quadrilateral is 360° A rhombus has rotation and reflection symmetry, therefore the opposite angles are equal.

∠D=∠F=115°

∠G=∠E=2(360−115−115)=2130=65°

Slide 8 - Slide

Equal angles in triangle and quadrilaterals

Isosceles triangle: 2 angles (base angles) are the same size Equilateral triangle: all 3 angles are the same size (60°) Rhombus/Parallelogram: opposite angles are equal Kite: 2 angles are the same size (on either side of the axis of symmetry) Square/Rectangle: all 4 angles are the same size (90°)